JPH0750136B2 - Frequency measurement method - Google Patents

Description

Detailed Description of the Invention

[0001]

FIELD OF THE INVENTION The present invention relates to frequency measurement and analysis, and more particularly to a method for measuring the frequency of individual spectral lines.

[0002]

2. Description of the Related Art A spectrum analyzer is an electronic measuring instrument for displaying the state of an electric signal in the frequency domain, that is, how the energy of the signal is distributed with respect to the frequency. . Although some spectrum analyzers are digital and some are analog, multiple filters are used to measure signal energy at different frequencies. An analog spectrum analyzer mixes an input signal and the frequency of a local oscillator to convert the frequency, and uses many physical filters having different frequency bands for this signal.

In a digital spectrum analyzer, the function of the same principle can be achieved by using a digital filter instead of the analog filter. Such a digital spectrum analyzer first samples and digitizes the signal under test to obtain a series of time domain digital samples. The sampling frequency at this time must be at least twice the bandwidth of interest. These time domain digital samples are provided to a group of digital bandpass filters, each tuned to a different frequency band to cover the frequency band of the input signal. Aliasing can be prevented by simultaneously sampling the output signals of these filters at an appropriate frequency proportional to each bandwidth.

One of the methods generally called DFT (Discrete Fourier Transform) or FFT (Fast Fourier Transform)
One can be used to form a group of filters. Details of such a method can be found in, for example, Oppenheim.
eim and Schafer's Digital Signal Processin
g) ”(Prentice Hall, 1975) and Crochiere and Rabiner's“ Multirate Digital Signal Processing (Multir
ate Digital Signal Processing) ”(Prentice
Hall, 1983) and many others.

As described in Chapter 7 of the above-mentioned document "Multirate Digital Signal Processing", there is a method of changing the time recording length M and the number K of filter groups. According to the method of polyphase structure, the value of M can be set to an arbitrary multiple of K. Weighted overlap add structure (WeightedOv
In the method of erlap-add structure), it is possible to remove the restriction of multiples and set the value of M to a value other than multiples larger than K. However, as the value of M increases, the time recording length increases more and more, and the calculation load also increases.
There is a problem that the time and calculation resources required for the calculation of the T process become excessive.

The shape of each output filter characteristic, ie the frequency response or impulse response, is independent of the number of filters. The number of samples as the time recording data and the number of output filter groups can be selected, and can take different values. However, in order to realize the FFT algorithm, it is necessary that the number of filters be equal to an integer power of the radix of the FFT.

In order to achieve a frequency resolution of Fs / K in analysis of a predetermined range by using a plurality of separate but identical filters, in order to realize a filter bank covering the analysis range, the center frequency is It is necessary to have K filters which are adjusted in ascending order. If a more extensive analysis is required, then additional filter banks will need to be added. It is not practical to rapidly increase the scale of hardware in this way.

However, if the feasible hardware is fast enough, the number of filters is much smaller, eg m
It is also possible to configure the system with (m <K) filters. This can be realized by executing the operation equivalent to the K filters by using the m filters constituting the hardware in a time division manner. This time division process is
It can be implemented in either of two ways. According to the first method, by changing the center frequency of the hardware of a single bandpass filter, the hardware is changed to K / m.
It can be used in time division within the range of individual filters. According to the second method, the hardware of a single low pass filter can be used in a time division manner by detecting the input signal at different frequencies respectively corresponding to the center frequencies of the desired filters. These detected signals are re-modulated after passing through one low pass filter.

Although these two methods are equivalent, the first method changes the characteristics of the filter with respect to the signal, and the second method
In this method, the signal is changed with respect to the filter. FIG. 1 is a block diagram showing a hardware configuration equivalent to the latter method. In this conventional example, detection and re-modulation processing is executed at high speed for filters whose center frequencies are sequentially adjusted in ascending order, so that filters realized by one piece of hardware are used in a time-division manner and arranged at equal intervals. To achieve a function equivalent to that of a plurality of filtered filters. To achieve this, it is necessary to sample the output at a frequency of r * Fs / K. Here, Fs is the sampling frequency of the input signal, r is a constant determined by the characteristics of the filter, and K is the number of filters whose center frequencies are adjusted in ascending order over the desired analysis range. The relationship between this Fs and the analysis frequency range is
Determined by Nyquist's theory.

Various filter characteristics have been adopted by designers of analog spectrum analyzers. As one of the filters that have been used in the field of analog spectrum analyzers and radars, there is a Gaussian filter characteristic represented by the following mathematical formula 1.

[Equation 1]

It has been conventionally performed to add some functions to the characteristics of these filter groups, such as signal extraction and transient response functions. For example, Collins U.S. Pat. No. 3,774,201 "Time Compression Signal Processor"
r) "column 13, lines 14-19," a filter having a substantially rectangular characteristic curve is suitable for direct spectral analysis, but one problem with radar systems is that Is to extract a signal component from a state in which there is a lot of noise. A Gaussian filter is more suitable for extracting a signal component in this way. "

US Pat. No. 461 by Mossey.
No. 0540 "Frequency Burst Analyzer (Frequency
Burst Analyzer) "discloses a plurality of filters for interpolating the position of a signal between the center frequencies of a filter group. In column 5, lines 7 to 62 of this publication, three methods for interpolating the position of a signal are described as means for regression analysis. The three methods disclosed in this patent are fairly complex, require a significant amount of computation time, and require four filter outputs for accurate results.

Therefore, it is an object of the present invention to provide a measuring method suitable for a spectrum analyzer of either a digital type or an analog type which can measure the frequency of a spectral line at high speed and accurately.

[0014]

SUMMARY OF THE INVENTION The present invention provides a method suitable for both digital and analog spectrum analyzers that measures the frequency of spectral lines quickly and accurately. According to the first method, the center frequencies fk1 and fk2
The signal under test is supplied to a pair of Gaussian filters each of which has a logarithmic value, the logarithmic value of the output of each pair of the Gaussian filters is calculated, and the difference ΔdB between the logarithmic values of the pair is calculated. The frequency is measured by linearly interpolating between the filter center frequencies fk1 and fk2. That is, this calculation is represented by the following equations 2, 3, and 4.

[Equation 2]

[Equation 3]

[Equation 4] According to the second method of the present invention, the swept local oscillation frequency and the signal under measurement are mixed to generate mixed signals at the first and second time points, and these mixed signals are combined into one Gaussian signal.
By supplying the difference to the outputs of the filters and obtaining the difference between the outputs of the filters, the result equivalent to the first method is obtained.

[0015]

EXAMPLE A Gaussian function has the interesting property that it maintains its function when transformed between the time and frequency domains. Therefore, when the weighting coefficient data group that conforms to the Gaussian function of the following Equation 5 is input to the DFT means, the output of the Gaussian characteristic represented by the above Equation 1 is the DFT.
Occurs on the output filter of the means.

[Equation 5]

FIG. 2 is a block diagram showing the outline of the processing of one embodiment of the present invention. A signal containing a pure sine wave with an unknown frequency fx is input to the filter banks Gk0 to Gk-1. The center frequencies of these filters Gk0 to Gk-1 are f0 to fk-1, respectively. The unknown frequency fx is assumed to be a value between the center frequencies fk1 and fk2 of the Gaussian filters Gk1, 12 and Gk2, 14. Center frequency f
Gaussian filters Gk1, 12 of k1 generate an output signal ampl-k1 in response to an input signal. Similarly, a Gaussian filter Gk2, 14 having a center frequency fk2 produces an output signal ampl-k2 in response to an input signal. Logarithmic amplifier 1
6 receives the signal ampl-k1 and outputs 20log-
Generate ampl-k1. Similarly, the logarithmic amplifier 18
Receives the signal ampl-k2 and outputs the output signal 20log-a
Generate mpl-k2. The subtraction circuit 20 is a logarithmic amplifier 1
It receives the signals from 6 and 18 and produces an output signal .DELTA.log-ampl which is proportional to the difference between these two input signals. The calculation means 22 calculates the unknown frequency fx by the interpolation calculation of the following Expression 2.

[Equation 2]

FIG. 3 is a flow chart showing the procedure of processing based on FIG. First, in step 30, the unknown frequency fx
Of the sine wave signals of which the center frequencies are fk1 and fk2 (fk1 <
Supply to two Gaussian filters with fx <fk2). This can be easily realized by using a plurality of filter groups that cover the entire frequency range as shown in FIG.

Equation 1 above generally represents the output signal of the filter. Based on this equation 1, equation 6 expressing the difference (decibel value) between the output signals of the two adjacent filters Gk1 and Gk2 is obtained. The following Expression 7 is an expression obtained by rearranging Expression 6, and ΔdB is a simplification of the left side of Expression 6.

[Equation 6]

[Equation 7]

In step 32, the logarithmic amplifier 16 of FIG.
And output signals 20 log-ampl-k 1 and 20 of 18
The respective terms on the left side of Expression 6 corresponding to log-ampl-k2 are measured. In the next step 34, 20 log-a
By calculating the difference between mpl-k1 and 20log-ampl-k2, the output signal Δlog of the subtraction circuit 20 of FIG.
-Calculate the value corresponding to ampl. These processes correspond to the equations 6 and 7 described above.

The above-mentioned expression 2 is calculated using the result of this expression 7. C1 and C2 in Expression 2 are defined by Expression 3 and Expression 4, respectively. Last step 36
Then, the unknown frequency fx is calculated by using the above-described equations 2, 3, and 4.

The logarithm of the Gaussian distribution becomes a parabola. Figure 4
FIG. 4 is a graph showing the output amplitude of the Gaussian filter on a logarithmic scale. The center frequency of the filter Gk1 is fk1 and the center frequency of the filter Gk2 is fk2. Frequency f
The x spectral line is measured with these two filters. The filter Gk1 generates the logarithmic amplitude signal ampl-k1 according to the input signal, and the filter Gk2 generates the logarithmic amplitude signal ampl-k2 according to the input signal. The frequency fx of the spectral line is calculated by using the difference Δampl between the ampl-k1 and the ampl-k2 in the above-mentioned formula 2.

The slope C1 of Equation 2 determines the resolution of the measurement frequency obtained by this method. When C1 is small, the change in amplitude with respect to the change in frequency, that is, Δamp
Since the value of l is also large, its measurement is easy. But C
When 1 becomes large, the value of Δampl becomes small with respect to the change in frequency. That is, the measurement frequency resolution decreases as C1 increases, and the measurement frequency resolution increases as C1 decreases.

FIG. 5 is a graph similar to FIG. 4, but in the case where σf in Expression 3 is smaller than that in FIG. Note that σf in Expression 3 represents the standard deviation of the measurement frequency. That is, as σf becomes smaller, the filter response of the graph of FIG. 4 becomes narrower as shown in FIG. Since the frequency measurement resolution is improved in this way, it is desirable to some extent that σf be small.

However, if σf becomes too small as shown in FIG. 5, the overlapping portion of the characteristics of the adjacent filters becomes insufficient. As can be seen from FIG. 5, the unknown output is a number fx
Is not within the response characteristic range of the filter Gk2. Figure 5
It is difficult to measure accurately even at a frequency slightly higher than the frequency of f x due to noise fluctuations. Therefore, there is a practical limit to how much the measurement resolution can be improved, and the resolution and noise are interrelated problems. That is, when trying to increase the resolution, the overlapping portion of the filter characteristics becomes insufficient, and measurement failure due to noise occurs. If the influence of noise is eliminated, the resolution will decrease.

As the standard deviation σf increases, not only the measurement frequency resolution decreases, but also the problem of signal leakage from non-adjacent signals arises. Although some overlap in the filter response is required, it can be seen that as the bandwidth of each filter increases, leakage from non-adjacent signals increases rapidly, as shown in FIG. Note that in FIG. 4, the spectral line just above the center frequency fk3 of the filter Gk3 represents the output characteristic of the filter Gk2. Such signal leakage limits how close the measured spectral line can be to other signals.

There are other factors to consider in choosing a value for the standard deviation σ f. If these Gaussian filter characteristics are selected so that the standard deviation σf in the frequency domain becomes small, there is a problem that the standard deviation σt in the time domain becomes large. This means that the impulse response of the filter becomes long, the multiplication and addition procedures increase, and it takes more time for the filter output to stabilize. When the time recording length is increased in this way, the limit of shortening the pulse width of the pulsed RF signal is limited, and it becomes difficult to fit the pulse within the time recording range. The time required to stabilize the filter output is the frequency of the sweep spectrum analyzer when one of the filter groups is used to change the center frequency for a certain spectrum line and the frequency comparison operation is performed. Limits the sweep speed of.

As described in the description of the prior art, all the filters in the filter group are replica filters of the low pass filter having the center frequency fc = 0. By setting the sensitivity level appropriately and the standard deviation σf in the frequency domain appropriately,
The standard deviation σt in the time domain is expressed by the following formula 8.

[Equation 8]

For a filter with a center frequency of 0, fc =
0 and tc = 0. Then, since the impulse response of the filter is determined only by the two parameters σt and tc,
The filter response can be determined from σf. As described in the section of the prior art, by detecting and remodulating the signal, the filter characteristic with the center frequency of 0 can be efficiently changed over a desired range, and a necessary filter bank can be realized.

However, the filter described above has an infinite impulse response characteristic. To limit this response it is necessary to apply some weighting function. This technology uses FIR
It is well known in the filter design field and many documents are known. The Oppenheim and Schaefer references mentioned above are also examples. Points to consider when selecting a particular window function are desired accuracy, S / N ratio, stabilization speed, and the like.

After the time record length is selected, the window function is applied to that time record. As a result, the actual response of the filter is compared to the desired response, and data indicating the difference between the desired response and the actual response for frequency is determined. The difference between the desired and the actual response of this filter is examined over two domains, time and frequency, to see how exactly the design criteria were realized. Within the passband of the filter, the difference between the desired response and the actual response indicates how well the actual result fits the desired σf. In the non-passing region of the filter, the difference between the desired response and the actual response indicates how poorly the sidelobe component is suppressed. In the latter case, if the suppression is insufficient, the process can be adjusted appropriately by either increasing the window length or looking for a more suitable window function.

Using either of these methods or C1
By adjusting the values of C2 and C2, the degree of approximation to the desired standard deviation σf can be improved. As a result, it is possible to accurately convert the actual value of Δlog-ampl into the correct frequency value. The corrected values of C1 and C2 are
It can be obtained by performing the least-squares approximation of the value of the above equation 2 to the actual value until the error becomes sufficiently small.

FIG. 6 is a graph showing the response of the filter output when the swept local oscillator 40 frequency sweeps the signal twice over the bandwidth of the filter. Thus, the present invention can also be realized by using one Gaussian filter and frequency sweeping an unknown spectral line by means of a swept local oscillator. In this case as well, the frequency fx of the unknown frequency spectrum line is calculated using Equations 2, 3, and 4.
To calculate. However, for fk1 and fk2, the following formulas 9 and 10 are replaced.

[Equation 9]

[Equation 10]

FIG. 7 is a block diagram showing the configuration of another embodiment of the present invention when only one Gaussian filter is used. In order to implement the invention with a single Gaussian filter 44, the unknown input signal fx is mixed in the mixer 42 with the output frequency of the swept local oscillator 40. At the time point t1, the mixed signal (fx-fLOt1) becomes the Gaussian filter 44.
Entered in. The output amp of this Gaussian filter 44
l-LOt1 is supplied to the logarithmic amplifier 46, and 20 log-
ampl-LOt1 is generated. This analog signal is
After being converted into a digital signal by the A / D (analog / digital) converter 48, it is stored in the memory 50.

At another time t2, the mixed signal (fx-fLOt2) is output from the mixer 42 and supplied to the Gaussian filter 44. The output of this filter ampl-LOt2
Is 20 log-ampl-LOt by the logarithmic amplifier 46.
Converted to 2. This analog signal is also stored in the memory 50 after being converted into a digital value.

The calculating means 52 includes the digital data 20log-ampl-LOt1 and 2 stored in the memory 50.
0log-ampl-LOt2 is searched and Δlog-am
Calculate pl. The value of the unknown frequency fx is this Δlo
The calculation can be performed using the value of g-ampl and the equations 2, 3 and 4 into which the above equations 9 and 10 are substituted.

In this method, C1 is proportional to the square of the standard deviation of the Gaussian filter, and the local oscillation frequency fLOt1
And fLOt2 are inversely proportional to the product of the common logarithm of e. C2 is the sum of f and the average value of the local oscillation frequencies fLOt1 and fLOt2 at the times t1 and t2. Here, f is the center frequency of the Gaussian filter.

A / D converter 48 and memory 50 are merely examples. As another example, if implemented in an analog circuit, the output of the logarithmic amplifier of the first measurement of the Gaussian filter output (time t1) is switched and delayed to a second measurement of the Gaussian filter output (time t2). ) Time is adjusted, and these two signals are supplied to the analog comparator functioning as a subtraction circuit to obtain Δlo.
The g-ampl signal may be obtained.

Although the preferred embodiments of the present invention have been described above, the present invention is not limited to the embodiments described herein, and various modifications and changes can be made as necessary without departing from the gist of the present invention. It will be apparent to those skilled in the art that changes can be made. In particular, the analog filter bank
A digital filter may be used, or a logarithmic scale other than the decibel value may be used when the above mathematical expression is appropriately changed.

[0039]

According to the first aspect of the present invention, the difference between the signals passed through the two Gaussian filters and the logarithmic amplifier is obtained, and linear interpolation is performed between the center frequencies of the Gaussian filters. Can measure frequency. According to the second aspect of the invention, the swept local frequencies at the first time point and the second time point are mixed with the signal under measurement, and these signals are supplied to one Gaussian filter, converted into a logarithmic value, and converted into a logarithmic value. By obtaining the difference, the frequency can be easily measured by the same calculation. The present invention is suitable for a spectrum analyzer of either analog type or digital type.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a conventional example.

FIG. 2 is a block diagram showing a configuration of an exemplary embodiment of the present invention.

FIG. 3 is a flowchart showing a procedure of an embodiment of the present invention.

FIG. 4 is a frequency-logarithmic graph representing an example of the response of the filter of FIG.

FIG. 5 is a graph showing a filter response when the value of σf is different from that of FIG.

FIG. 6 is a graph showing an example of a Gaussian filter response obtained by frequency sweeping twice with a swept local oscillator.

FIG. 7 is a block diagram showing the configuration of another embodiment according to the present invention.

[Explanation of symbols]

 10, 12, 14, 24, 44 Gaussian filter 16, 18, 46 Logarithmic amplifier 20 Subtraction circuit 22, 52 Calculation means

Claims (2)

[Claims] 1. A device having center frequencies fk1 and fk2, respectively.
The signals to be measured are supplied to a pair of Gaussian filters, the logarithmic values of the pair of outputs of the Gaussian filter are obtained, and the difference Δlog-ampl of the pair of logarithmic values is obtained, and fx = Δlog-ampl × C1 + C2 Where C1 is proportional to the square of the standard deviation σf of the Gaussian filter, and the center frequency difference (fk1
A frequency measuring method characterized in that the frequency fx of the signal under measurement is measured by calculating a constant C2 = (fk1 + fk2) / 2, which is inversely proportional to −fk2). 2. A local frequency fLOt1 at a first time point of a swept local oscillator is mixed with a signal under test to generate a first mixed signal, and the first mixed signal is supplied to a Gaussian filter having a center frequency f. A first logarithmic value proportional to the logarithm of the output of the Gaussian filter, mixing the local frequency fLOt2 at the second time point of the swept local oscillator with the signal under test to generate a second mixed signal, The second mixed signal is supplied to the Gaussian filter, the second logarithmic value proportional to the logarithm of the output of the Gaussian filter is obtained, the difference Δlog-ampl between the first and second logarithmic values is obtained, and fx = Δlog -ampl × C1 + C2 where C1 is proportional to the square of the standard deviation σf of the Gaussian filter, and the difference between the local oscillation frequencies (fLOt1−fLOt2)
A frequency measuring method characterized in that the frequency fx of the signal under measurement is measured by calculating a constant C2 = (fLOt1 + fLOt2) / 2 + f which is inversely proportional to.